Explain whose point of view as owner the FCFE approach takes

The FCFE approach values equity from the viewpoint of an owner who can decide how cash is used. FCFE is what the company could pay its shareholders after all obligations and investment, whether or not it actually does so, whereas dividends are what the board chooses to pay. A minority investor receives only the dividends, but a controlling shareholder can direct the company to distribute its free cash flow, so an FCFE value is generally taken to reflect a control perspective. This makes FCFE natural for takeover analysis, and explains why a minority stake may be worth less than its share of the FCFE value when dividends are far below FCFE. The trap is assuming dividends and FCFE must be the same.